It is common practice after workpieces have been produced to inspect them on a coordinate positioning apparatus, such as a coordinate measuring machine (CMM) having a movable probe head within a working volume of the machine.
In a conventional three-dimensional measuring machine, the probe head is supported for movement along three mutually perpendicular axes (in directions X, Y and Z).
In a simple form of the machine a suitable transducer mounted parallel to each axis is able to determine the position of the probe head relative to a base of the machine and, therefore, to determine the coordinates of a measurement point on an object being approached by the probe.
There are several possible sources of error if such a technique is employed. Lack of straightness in movement and of orthogonality of the axes is one major cause of such errors. A further cause of error is the angular rotation of the carriages about axes perpendicular to their directions of movement. Such errors, often referred to as Abbé errors, depend not only upon rotation but also upon a lateral offset in the linear drive mechanisms.
Further sources of errors may include external influences like vibrations, temperature variation, pressure variation, humidity variation, aging of components of the CMM-frame-structure, etc.
Particularly, the following error factors may occur:                scale errors on axes,        horizontal straightness errors on axes,        vertical straightness errors on axes,        pitching errors on axes,        yawing errors on axes,        rolling errors on axes, and        angular errors between axes.        
Also, weaknesses in the frame structure of the CMM—which may lead to a bending of e.g. the legs or the bridge of the CMM—cause errors.
Many attempts have been made to provide correction for the various sources of error referred to. For example, it is known to introduce a deliberate and known error into the transducers by various means. However, such corrections only apply for a given location in the measuring volume.
An alternative technique is to calibrate the machine, measuring the errors existing at various points and storing these so that they may be applied when the machine is actually used. Exemplarily in connection with such calibration methods, for each axis (x, y, z) and each linear drive mechanism, some axis dependent geometrical errors are measured—e.g. pitch, yaw, straightness (in two orthogonal axis) and roll. That measurement can be done by some kind of increment (for example every 20 mm), the gathered data is stored in a calibration table (in the machine or the software) and is used when running the machine in such a way, that the data in the table corrects the geometrical errors depending on the position. In addition to this there is of course the angularity between the axis (x, y, z) and some scale factor for each axis. The calibration method is usually carried out on a complete assembled machine.
As may be imagined, such a calibration process is lengthy, especially for a large machine. However, any “settling” of the machine during use would invalidate the calibrations. Another drawback with the calibration methods is that they will only take care of fully repeatable errors. It is also necessary to calibrate the probe during the same conditions as in the working state of the machine. This means that if the machine runs with 100 mm/sec, the calibration procedure also should be performed with that speed, and if—by some reason—a change of the running speed is necessary, a recalibration of the machine with this new speed would be required.
Another aspect which has to be considered is that accelerations of the probe cause dynamic deflections of the coordinate measuring machine which in turn cause measurement errors. These measurement errors may be reduced by taking measurements at low accelerations. However, productivity demands an increased throughput as well as an increased inspection speed. Hence, the probe experiences higher accelerations during the measurements and larger dynamic structural deflections of the system—in particular the frame structure of the CMM—result. This causes inaccurate reporting of the X, Y, Z geometric position of the probe.
In particular, some coordinate measuring machines exhibit significant drive vibration at high speed. One source of error causing the vibration is the machine mechanical drive system. Errors caused by these vibrations (typically above 5 Hz) are not suitable for calculative methods of compensation for dynamic errors described above as the vibration causes non repeatable behaviour at high speed which causes measurement errors.
Furthermore, a variety of probes are employed in a coordinate measuring machine for measurements within the scale coordinate system, which includes reference scales arranged along axes that configure the three-dimensional measuring space. To provide the coordinate measuring machine with an improved measurement precision, the structure of the frame thereof is required to have a high static stiffness.
Exemplary, EP 1 559 990 discloses a coordinate measuring system and method of correcting coordinates measured in a coordinate measuring machine. Thereby, geometrical errors are measured while works with various weights are mounted on the coordinate measuring machine. Compensation parameters are derived from measured results per a weight of a work and stored. A compensation parameter corresponding to a weight of a work to be measured is appropriately read out to correct measured coordinates of the work to be measured.
As a further example, EP 1 687 589 discloses a method of error compensation in a coordinate measuring machine with an articulating probe head having a surface detecting device. The surface detecting device is rotated about at least one axis of the articulating probe head during measurement. The method comprises the steps of: determining the stiffness of the whole or part of the apparatus, determining one or more factors which relate to the load applied by the articulating probe head at any particular instant, and determining the measurement error at the surface sensing device caused by the load.
Also, GB 2 042 719 discloses a measuring apparatus having three mutually perpendicular axes, wherein errors due to rotations about the various axes are corrected.
Another approach for error correction of work piece measurements with a coordinate measuring machine (CMM) is disclosed in GB 2 425 840. Thereby, position measurements are taken with a work piece sensing probe, in which means of measuring acceleration are provided. The measurements are corrected for both high frequency (unrepeatable) errors such as those due to vibration, and low frequency (repeatable) errors such as those due to centrifugal forces on the probe. The correction method comprises measuring the work piece, determining repeatable measurement errors from a predetermined error function, error map or error look-up table, measuring acceleration and calculating unrepeatable measurement errors, combining the first and second measurement errors to determine total errors and correcting the work piece measurements using the total errors. The predetermined error map is calculated using an artefact of known dimensions.
It is also known to use accelerometers fitted in the probe (or Z-column) of the machine and in the base table (for a differential measurement). The displacements and errors of the probe-position are measured with double integration, and from that it will be possible to adjust the reading with the difference between the double integrated signal and the scales.
However, when using accelerometers, they will usually become noisy when the frequency is relatively low. This can give a bad signal to noise ratio. Furthermore, it may only be possible to measure differences during acceleration, which means that—in general—it may be necessary to calculate the acceleration from the scale position and to compare it with the measured acceleration, and double integrate the difference. However, this may not be enough information to accurately calculate the exact position of the probe. Using such a method also doesn't allow measuring static changes (i.e. friction in combination with dynamic changes will not be considered).